Three.js export option is sometimes disabled
In Blender there is a difference between active and selected,
typically its fine to think of active as last selected.

Notice when you select the object, its outline (or wire) color is brighter then other selected objects.

The poll only succeeds (i.e., the operator is only enabled) if bpy.context.active_object != None: see io_mesh_threejs/__init__.py:323.

This will be the case right after you deleted an object, imported models (e.g. OBJ) or certain operator calls. These operations can clear the active_object, although objects may still be selected.

Select any object (or set active_object to an object with python) before you open the File > Export panel.